Stellar Mass‐to‐Light Ratios and the Tully‐Fisher Relation

We have used a suite of simplified spectrophotometric spiral galaxy evolution models to argue that there are substantial variations in stellar mass-to-light ( M / L ) ratios within and among galaxies, amounting to factors of between 3 and 7 in the optical and factors of 2 in the near-infrared. Our models show a strong correlation between stellar M / L and the optical colors of the integrated stellar populations. Under the assumption of a universal spiral galaxy initial mass function (IMF), relative trends in model stellar M / L with color are robust to uncertainties in stellar population and galaxy evolution modeling, including the effects of modest bursts of star formation. Errors in the dust-reddening estimates do not strongly affect the final derived stellar masses of a stellar population. We examine the observed maximum disk stellar M / L ratios of a sample of spiral galaxies with accurate rotation curves and optical and near-infrared luminosity profiles. From these observed maximum disk M / L ratios we conclude that a Salpeter IMF has too many low-mass stars per unit luminosity but that an IMF similar to the Salpeter IMF at the high-mass end with less low-mass stars (giving stellar M / L ratios 30% lower than the Salpeter value) is consistent with the maximum disk constraints. Trends in observed maximum disk stellar M / L ratios with color provide a good match to the predicted model relation, suggesting that the spiral galaxy stellar IMF is universal and that a fraction of (particularly high surface brightness) spiral galaxies may be close to maximum disk. We apply the model trends in stellar M / L ratio with color to the Tully-Fisher (T-F) relation. We find that the stellar mass T-F relation is relatively steep, has modest scatter, and is independent of the passband and color used to derive the stellar masses, again lending support for a universal IMF. The difference in slope between the optical (especially blue) and near-infrared T-F relations is due to the combined effects of dust attenuation and stellar M / L variations with galaxy mass. Assuming the Hubble Space Telescope Key Project distance to the Ursa Major Cluster and neglecting the (uncertain) molecular gas fraction, we find that the baryonic T-F relation takes the form M baryon ∝ V 3.5 (with random and systematic 1 σ slope errors of ~0.2 each) when using a bisector fit and rotation velocities derived from the flat part of the rotation curve. Since we have normalized the stellar M / L ratios to be as high as can possibly be allowed by maximum disk constraints, the slope of the baryonic T-F relation will be somewhat shallower than 3.5 if all disks are substantially submaximal.